McKenzie notched up his fourth Test century to help the tourists to 331 for five in their second essay, a lead of 254 runs, before the rival captains agreed to stop the proceedings just after tea.
The 32-year-old, who notched 226 during a world record 415-run opening partnership with skipper Graeme Smith against Bangladesh earlier this month, hit 13 fours and a six and added 157 runs for the second wicket with Hashim Amla.
Amla, South Africa's top scorer in the first innings with 159, struck a chancy 81.
Indian off spinner Harbhajan Singh took three for 101 and claimed eight wickets in the match.
India scored 627 in reply to South Africa's first innings 540 all out on a flat pitch.
Opener Virender Sehwag hit an Indian record 319 and Dravid 111 for his 25th hundred before fast bowlers Dale Steyn and Makhaya Ntini shared seven wickets to restrict their first innings lead to 87 runs on the fourth day.
The second Test starts in Ahmedabad on Thursday.